Hidden symmetries and Killing tensors on curved spaces

Details Hidden symmetries and Killing tensors on curved spaces Hidden symmetries and Killing tensors on curved spaces

2008-11-21

arxiv.org/abs/0811.3478v1

Phys.Atom.Nucl.73:1925-1930,2010

Physics

Mathematical Physics

12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia, August 2008

Scientific paper

10.1134/S1063778810110141

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.

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